Note:
this new version has 900+ pages (!).
Please save trees and don't print all of it at once, we will only cover some small parts of
the notes in the course
Prerequisites
Covariant Formulation of Special Relativity (Minkowski Geometry, Lorentz Tensor Algebra etc.)
Classical Field Theory (Action Principles for Fields)
Multivariable Calculus
Contents
Physical and Mathematical Foundations of General Relativity
If you are planning to take the exam in January / February 2019, please
sign up for the exam via KSL until latest January 30th! (If you are
planning to take the exam at a much later stage, there is no need to sign up now.)
Dates:
Theory Master Students: February 04/05/06. See the
information below for available slots and contact me for
preferred time.
Others: If you are happy with these dates, please also
sign up for one of these slots. If not,
contact me for individual appointments. (These appointments will then also appear in the list below.)
Confirmed/agreed Dates and Time:
February 04, 11h: Igor Jurosevic
February 04, 12h:
February 04, 14h: Rafael Moser
February 04, 15h:
February 05, 11h: Barbara Jenny
February 05, 12h:
February 05, 14h: Antea Doriot
February 05, 15h:
February 06, 11h: Tabea Krucker
February 06, 12h: Linus Vogt
February 06, 14h: Merlin Utiger
February 06, 15h: Omar Celikbas
February 21, 11h: Caroline Haslebacher
February 21, 12h: Omar Celikbas
February 24, 14h: Anja Gauch (postponed to March)
February 24, 15h: Jo Ann Egger (postponed to March)
Further Information:
Exams take place in my office (220a).
Upon request, we can organise a Question (and Answer!) Session some time in January. Let me know.
Feel free to come to my office (with or without prior appointment)
if you have any questions.
However:
I will not answer questions via e-mail - my experience is that this
is likely to lead to more confusion than understanding.
Contents: During each exam, I will try to touch upon the following 4 general
subjects:
Dynamics of Particles and Fields in a Gravitational Field:
metric and gravitational field, geodesic equation, action principle,
Newtonian limit, redshift, conserved charges, minimal coupling, scalar
field, definition of energy momentum tensor etc
Dynamics of the Gravitational Field:
Einstein equations and their main properties (definition of Riemann, Ricci etc,
number of equations, role of Bianchi, ...). Einstein-Hilbert action. vacuum
Einstein equations etc
Schwarzschild Metric and the Solar System:
main properties of the metric; derivation of the effective potential and orbit
equations;
main qualitative difference(s) between Kepler and GR orbits etc
Schwarzschild Metric and Black Holes:
significance of r=2m: what happens or does not happen there; tortoise and Eddington-Finkelstein
coordinates; freely falling versus static observers; behaviour of lightcones; Kruskal diagram etc
In the Spring Semester (FS20), I will give a Master/Graduate
Course on Selected Advanced Topics in General Relativity (more on Black Holes
and other fun things):
Preliminary Schedule: Weeks 1-7 of the Semester, Thursday 14-17h
Preliminary List of Topics:
Review of the Schwarzschild Black Hole
Guided Visit to the Zoo of Black Hole Solutions
Classical Theory of Black Holes
Carter-Penrose Conformal Diagrams
Unruh Effect, Hawking Temperature and Hawking Radiation
Aspects of Black Hole Entropy and Black Hole Thermodynamics
Outlook/Wild Stuff: Information Paradox / Firewalls / AdS/CFT / Black Holes and Quantum Information Theory etc
Information for Theory Master Students:
Please regard this course as an optional additional course.
The main Specialist Course offered by the ITP this semester is
the course Conformal Field Theory by Susanne Reffert, which you
are strongly encouraged to attend.
In order to compensate the reduced number of hours compared to
a regular Specialist Course, to acquire the ECTS for this course you
will need to do a homework project / presentation based on the contents of the course. Details to be discussed at a later stage.
Highly Recommended Literature
Excellent Introductory (Undergraduate) Text
J.B. Hartle: Gravity, An introduction to Einstein's General Relativity
Elegant Modern Slightly More Advanced Books
R.M. Wald: General Relativity
S. Carroll: Spacetime and Geometry, an Introduction to General Relativity
Classics
C.W. Misner, K.S. Thorne, J.A. Wheeler: Gravitation
S. Weinberg: Gravitation and Cosmology
Other Personal Favourites
R.U. Sexl, H.K. Urbantke: Gravitation und Kosmologie
N. Straumann: General Relativity
S.W. Hawking, G.F.R. Ellis: The Large Scale Structure of Space-Time
E. Poisson: A Relativist's Toolkit
Other Recommended Recent/New Books
A. Zee: Einstein Gravity in a Nutshell
GR Lectures Notes on the WWW and related Online Resources
Note: the resources mentioned below are approved/recommended. If you come across, and want to use, some other
online resources, please come and show them to me (also in GR, there is much more low- than high-quality
stuff floating around on the WWW and it may not always be easy for you to decide at first sight which is which).
Please let me know of any broken (no longer existing) links.
Is our Universe a Black Hole? NO And since I get
asked this question again and again (as if there weren't more interesting questions), usually by people
who understand neither cosmology nor black holes, here are some links:
